Discharge Coefficients of a Preswirl System in Secondary Air Systems

2001 ◽  
Vol 124 (1) ◽  
pp. 119-124 ◽  
Author(s):  
M. Dittmann ◽  
T. Geis ◽  
V. Schramm ◽  
S. Kim ◽  
S. Wittig
Keyword(s):  
Pressure Ratio ◽  
Rotating System ◽  
Free Expansion ◽  
Discharge Coefficients ◽  
Discharge Behavior ◽  
Secondary Air ◽  
Absolute Frame ◽  
Definition Of ◽  
Work Done ◽  
Good Agreement

The discharge behavior of a “direct-transfer” preswirl system has been investigated experimentally. The influences of the pressure ratio and the swirl ratio as well as the influence of the receiver and stator geometry were investigated. The discharge coefficients of the preswirl nozzles are given in the absolute frame of reference. The definition of the discharge coefficient of the receiver holes is applied to the rotating system in order to consider the work done by the rotor. Numerical calculations carried out for a free expansion through the stationary preswirl nozzles show very good agreement with experimental data.

Discharge Coefficients of a Pre-Swirl System in Secondary Air Systems

2001 ◽  
Author(s):  
M. Dittmann ◽  
T. Geis ◽  
V. Schramm ◽  
S. Kim ◽  
S. Wittig
Keyword(s):  
Pressure Ratio ◽  
Rotating System ◽  
Free Expansion ◽  
Discharge Coefficients ◽  
Secondary Air ◽  
Absolute Frame ◽  
Definition Of ◽  
Work Done ◽  
Discharge Behaviour ◽  
Good Agreement

The discharge behaviour of a “direct-transfer” pre-swirl system has been investigated experimentally. The influences of the pressure ratio and the swirl ratio as well as the influence of the receiver and stator geometry were investigated. The discharge coefficients of the pre-swirl nozzles are given in the absolute frame of reference. The definition of the discharge coefficient of the receiver holes is applied to the rotating system in order to consider the work done by the rotor. Numerical calculations carried out for a free expansion through the stationary pre-swirl nozzles show very good agreement with experimental data.

Discharge Coefficients of Rotating Short Orifices With Radiused and Chamfered Inlets

2004 ◽  
Vol 126 (4) ◽  
pp. 803-808 ◽  
Author(s):  
M. Dittmann ◽  
K. Dullenkopf ◽  
S. Wittig
Keyword(s):  
Discharge Coefficient ◽  
Pressure Ratio ◽  
Reynolds Numbers ◽  
Frame Of Reference ◽  
Efficient Operation ◽  
Discharge Coefficients ◽  
Wide Range ◽  
Secondary Air ◽  
Cooling Air ◽  
Actual Geometry

The secondary air system of modern gas turbine engines consists of numerous stationary or rotating passages to transport the cooling air, taken from the compressor, to thermally high loaded components that need cooling. Thereby the cooling air has to be metered by orifices to control the mass flow rate. Especially the discharge behavior of rotating holes may vary in a wide range depending on the actual geometry and the operating point. The exact knowledge of the discharge coefficients of these orifices is essential during the design process in order to guarantee a well adapted distribution of the cooling air inside the engine. This is crucial not only for a safe and efficient operation but also fundamental to predict the component’s life and reliability. In this paper two different methods to correlate discharge coefficients of rotating orifices are described and compared, both in the stationary and rotating frame of reference. The benefits of defining the discharge coefficient in the relative frame of reference will be pointed out. Measurements were conducted for two different length-to-diameter ratios of the orifices with varying inlet geometries. The pressure ratio across the rotor was varied for rotational Reynolds numbers up to ReΦ=8.6×105. The results demonstrate the strong influence of rotation on the discharge coefficient. An analysis of the complete data shows significant optimizing capabilities depending on the orifice geometry.

Discharge Coefficients of Rotating Short Orifices With Radiused and Chamfered Inlets

2003 ◽  
Author(s):  
M. Dittmann ◽  
K. Dullenkopf ◽  
S. Wittig
Keyword(s):  
Discharge Coefficient ◽  
Pressure Ratio ◽  
Reynolds Numbers ◽  
Frame Of Reference ◽  
Efficient Operation ◽  
Discharge Coefficients ◽  
Wide Range ◽  
Secondary Air ◽  
Cooling Air ◽  
Actual Geometry

The secondary air system of modern gas turbine engines consists of numerous stationary or rotating passages to transport the cooling air, taken from the compressor, to thermally high loaded components that need cooling. Thereby the cooling air has to be metered by orifices to control the mass flow rate. Especially the discharge behavior of rotating holes may vary in a wide range depending on the actual geometry and the operating point. The exact knowledge of the discharge coefficients of these orifices is essential during the design process in order to guarantee a well adapted distribution of the cooling air inside the engine. This is crucial not only for a safe and efficient operation but also fundamental to predict the component’s life and reliability. In this paper two different methods to correlate discharge coefficients of rotating orifices are described and compared, both in the stationary and rotating frame of reference. The benefits of defining the discharge coefficient in the relative frame of reference will be pointed out. Measurements were conducted for two different length-to-diameter ratios of the orifices with varying inlet geometries. The pressure ratio across the rotor was varied for rotational Reynolds numbers up to Reφ = 8:6 × 105. The results demonstrate the strong influence of rotation on the discharge coefficient. An analysis of the complete data shows significant optimising capabilities depending on the orifice geometry.

Characteristics of Discharge Coefficient in a Rotating Disk System

1999 ◽  
Vol 121 (4) ◽  
pp. 663-669 ◽  
Author(s):  
D. J. Maeng ◽  
J. S. Lee ◽  
R. Jakoby ◽  
S. Kim ◽  
S. Wittig
Keyword(s):  
Discharge Coefficient ◽  
Three Dimensional ◽  
Compressibility Factor ◽  
Rotating Disk ◽  
Operating Conditions ◽  
Disk System ◽  
Rotating System ◽  
Rotor Disk ◽  
Discharge Behavior ◽  
Definition Of

The discharge coefficient of a long orifice in a rotating system is measured to examine the rotational effect on discharge behavior. The rotating system is comprised of a rotating disk and two stators on both sides of the rotating disk. Test rig is constructed to simulate the real turbine operating conditions. Pressure ratios between upstream and downstream cavities of the orifice range from 1.05 to 1.8, and rotational speed of the rotor disk is varied up to 10,000 rpm. The orifice hole bored through the rotor disk has length-to-diameter ratio of 10. For a better interpretation of discharge behavior, three-dimensional velocity field in the downstream and upstream cavities of the rotor is measured using a Laser Doppler Velocimetry. A new definition of the rotational discharge coefficient is introduced to consider the momentum transfer from the rotor to the orifice flow. Additional loss in the discharge coefficient due to pressure loss in the orifice hole at the inlet and exit regions is quantitatively presented in terms of the Rotation number and the compressibility factor. The effect of corner radiusing at the orifice inlet is also investigated at various rotational conditions.

scholarly journals Characteristics of Discharge Coefficient in a Rotating Disk System

1998 ◽  
Author(s):  
D. J. Maeng ◽  
J. S. Lee ◽  
R. Jakoby ◽  
S. Kim ◽  
S. Wittig
Keyword(s):  
Discharge Coefficient ◽  
Three Dimensional ◽  
Compressibility Factor ◽  
Rotating Disk ◽  
Operating Conditions ◽  
Disk System ◽  
Rotating System ◽  
Rotor Disk ◽  
Discharge Behavior ◽  
Definition Of

The discharge coefficient of a long orifice in a rotating system is measured to examine the rotational effect on discharge behavior. The rotating system is comprised of a rotating disk and two stators on both sides of the rotating disk. Test rig is constructed to simulate the real turbine operating conditions. Pressure ratios between upstream and downstream cavities of the orifice range from 1.05 to 1.8, and rotational speed of the rotor disk is varied up to 10,000 rpm. The orifice hole bored through the rotor disk has length-to-diameter ratio of 10. For a better interpretation of discharge behavior, three-dimensional velocity field in the downstream and upstream cavities of the rotor is measured using a Laser Doppler Velocimetry. A new definition of the rotational discharge coefficient is introduced to consider the momentum transfer from the rotor to the orifice flow. Additional loss in the discharge coefficient due to pressure loss in the orifice hole at the inlet and exit regions is quantitatively presented in terms of the Rotation number and the compressibility factor. The effect of comer radiusing at the orifice inlet is also investigated at various rotational conditions.

Investigation of Recirculating Casing Treatment for Low-Pressure Ratio Mixed-Flow Micro-Compressor

2020 ◽  
Author(s):  
Kewei Xu ◽  
Gecheng Zha
Keyword(s):  
Pressure Ratio ◽  
Numerical Approach ◽  
Efficiency Loss ◽  
Stall Margin ◽  
Design Point ◽  
Casing Treatment ◽  
Final Design ◽  
Upstream Flow ◽  
Total Pressure Ratio ◽  
Good Agreement

Abstract This paper investigates the recirculating casing treatment (RCT) of a low total pressure ratio micro-compressor to achieve stall margin enhancement while minimizing the design point efficiency penalty. Three RCT injection and extraction configurations are studied, including combined slot-duct, ducts only, and slot only. The numerical approach is validated with a tested micro-compressor using RCT. A very good agreement is achieved between the predicted speedlines and the measured results. To minimize the design point efficiency loss, it is observed that the optimal location of extraction and injection is where the recirculated flow rate can be minimized at the design point. To maximize stall margin, extraction location should favor minimizing the tip blockage such as at the location where the tip flow separation of the baseline blade is fully developed. In addition, the slot configuration that generates pre-swirl to the upstream flow is beneficial to improve stall margin due to reduced incidence. The highest stall margin enhancement achieved is 9.49% with the slot geometry that has the extraction at the 62%C chordwise location, but has a design point efficiency loss of 1.9%. Overall, a small efficiency penalty of 0.6% at the design point is achieved for the final design with the stall margin increased by 6.2%.

The Development of Virtual Concurrent Engineering and its Application to Stamped Products

1992 ◽  
Author(s):  
J. Schmitz ◽  
S. Desa
Keyword(s):  
Product Development ◽  
Design Optimization ◽  
Concurrent Engineering ◽  
Extensive Study ◽  
Engineering Method ◽  
Engineering Product ◽  
Development Method ◽  
Computer Based ◽  
Definition Of ◽  
Work Done

Abstract It is well-known that so-called Concurrent Engineering is a desirable alternative to the largely sequential methods which tend to dominate most product development methods. However, the proper implementation of a concurrent engineering method is still relatively rare. In order to facilitate the development of a reliable concurrent engineering product development method, we start with a careful definition of concurrent engineering and, after an extensive study of all of product development, we propose three criteria which ideal concurrent engineering must satisfy. However, for labor, time, and overall cost considerations, ideal concurrent engineering is infeasible. Instead, we propose a computer-based environment which, by being constructed in accordance with the three criteria, attempts to approach ideal concurrent engineering. The result is the Virtual Concurrent Engineering method and computer implementation environment. This product development method and computer-based implementation system provide the detailed, structured information and data needed to optimally balance the product with respect to the main product development parameters (e.g., manufacturing costs, assembly, reliability). This important information includes re-design suggestions to improve the existing design. The designer can directly apply these re-design suggestions for design optimization, or he can use the results as input into a more complex design optimization or design parameterization function of his own. To demonstrate Virtual Concurrent Engineering, we use it to refine earlier work done by the authors in the Design for Producibility of stamped products. We discuss, in some detail, the results of applying Design for Producibility to complex stampings, including process plans and product producibility computations.

ALTERNATIVE COEFFICIENT OF CONCORDANCE IN CASE OF CONNECTED RANKS

2021 ◽  
pp. 40-45
Author(s):  
Ю.В. Лубенец
Keyword(s):  
Expert Opinion ◽  
Special Kind ◽  
Statistical Characteristics ◽  
Expert Survey ◽  
Complete Consistency ◽  
Expert Opinions ◽  
Coefficient Of Concordance ◽  
Definition Of ◽  
Two Stages ◽  
Good Agreement

Рассматривается оценка согласованности мнений экспертов при проведении экспертного опроса. Наиболее часто в качестве такой оценки применяется коэффициент конкордации Кендалла. Однако этот коэффициент не может в полной мере применяться для установления хорошей согласованности мнений экспертов, поскольку он показывает только отклонение от случаев полной несогласованности. Для устранения данного недостатка может рассматриваться альтернативный коэффициент конкордации, оценивающий близость сумм рангов альтернатив к случаю полной согласованности. Здесь дается определение этого коэффициента при наличии связанных рангов. Сложность определения заключается в том, что в этом случае наблюдается несколько случаев полной согласованности с различными суммами рангов. Определение альтернативного коэффициента конкордации при наличии связанных рангов проводится в два этапа. Сначала вводится его определение для упорядоченных таблиц специального вида и показывается его совпадение с коэффициентом конкордации Кендалла в этом случае. После дается определение альтернативного коэффициента конкордации в общем случае и показывается более простая формула его вычисления. Далее приводятся некоторые примеры сравнений значений рассматриваемых коэффициентов конкордации, их статистических характеристик и гистограмм The article considers evaluation of expert opinion consistency when conducting an expert survey. The most commonly used score is Kendall's coefficient of concordance. However, this coefficient cannot be fully applied to establish good agreement of expert opinions, as it only shows deviations from cases of complete inconsistency. To eliminate this drawback, an alternative concordance coefficient can be considered, which estimates the proximity of the sums of the ranks of the alternatives to the case of complete consistency. The article gives the definition of this coefficient in the presence of connected ranks. The difficulty of this definition lies in the fact that in this case there are several cases of complete consistency with different sums of ranks. Definition of the alternative coefficient of concordance in the presence of tied ranks is carried out in two stages. First, its definition for ordered tables of a special kind is introduced and its coincidence with Kendall's coefficient of concordance in this case is shown. After that, the definition of the alternative coefficient of concordance in the general case is given and a simpler formula for its calculation is shown. Below are some examples of comparisons of the values of the considered concordance coefficients, their statistical characteristics, and histograms

Next Generation Turbine Testing at DLR

2017 ◽  
Author(s):  
Hans-Jürgen Rehder ◽  
Andreas Pahs ◽  
Martin Bittner ◽  
Frank Kocian
Keyword(s):  
Test Section ◽  
Power Plants ◽  
Pressure Ratio ◽  
Thermodynamic Cycle ◽  
Calibration Procedure ◽  
Test Facility ◽  
Next Generation ◽  
High Pressure Ratio ◽  
Secondary Air ◽  
German Aerospace

Axial turbines for aircraft engines and power plants have reached a very high level of development. Further improvements, in particular in terms of higher efficiency and reduced number of blades and stages, resulting in higher loads, are possible, but can only be achieved through a better understanding of the flow parameters and a closer connection between experiment and numerical design and simulation. An analysis of future demands from the industry and existing turbine research rigs shows that there appears a need for a powerful turbine test rig for aerodynamic experiments. This paper deals with the development and built up of a new so called Next Generation Turbine Test Facility (NG-Turb) at the German Aerospace Center (DLR) in Göttingen. The NG-Turb is a closed-circuit, continuously running facility for aerodynamic turbine investigations, allowing independent variation of engine relevant Mach and Reynolds numbers. The flow medium (dry air) is driven by a 4-stage radial gear compressor with a high pressure ratio and a wide inlet volume flow range. In a first stage the NG-Turb test section will allow investigations on single shaft turbines up to 2½ stages. In a further expansion stage the NG-Turb will be equipped with a second independent shaft system, then enabling experiments with configurations of high and low (or intermediate) pressure turbines and in particular offering the possibility for investigations at counter rotating turbines. Secondary air for cooling investigations can be provided by auxiliary screw compressors. Mass flow through the Turbine is determined redundantly with an uncertainty of about ±0.3%, using well calibrated Venturi nozzles upstream and downstream of the test section. The operation concept and main design features of the NG-Turb will be described and an overview of the applied standard measurement and data acquisition technics capturing efficiency, traverse data etc. will be given. Thermodynamic cycle calculations have been performed in order to simulate the flow circuit of the NG-Turb and to access whether turbine operating points can be driven within the performance map of the compressor system. Finally the calibration procedure for the Venturi nozzles, which has been conducted during the commissioning phase of the NG-Turb by applying a special calibration test section, is explained and some results will be shown.

scholarly journals Asymptotic analysis for personalized Web search

2010 ◽  
Vol 42 (02) ◽  
pp. 577-604 ◽  
Author(s):  
Yana Volkovich ◽  
Nelly Litvak
Keyword(s):  
Web Search ◽  
Power Laws ◽  
User Preference ◽  
Importance Measure ◽  
Web Documents ◽  
Original Definition ◽  
Theoretical Predictions ◽  
Heavy Tailed ◽  
Definition Of ◽  
Good Agreement

PageRank with personalization is used in Web search as an importance measure for Web documents. The goal of this paper is to characterize the tail behavior of the PageRank distribution in the Web and other complex networks characterized by power laws. To this end, we model the PageRank as a solution of a stochastic equationwhere theRis are distributed asR. This equation is inspired by the original definition of the PageRank. In particular,Nmodels the number of incoming links to a page, andBstays for the user preference. Assuming thatNorBare heavy tailed, we employ the theory of regular variation to obtain the asymptotic behavior ofRunder quite general assumptions on the involved random variables. Our theoretical predictions show good agreement with experimental data.

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